Probing $f(R)$ gravity with PLANCK data on cluster pressure profiles

Analytical $f(R)$-gravity models introduce Yukawa-like corrections to the Newtonian potential in the weak field limit. These models can explain the dynamics of galaxies and cluster of galaxies without requiring dark matter. To test the model, we have computed the pressure profile of 579 X-ray galaxy clusters assuming the gas is in hydrostatic equilibrium within the potential well of the modified gravitational potential. We have compared those profiles with the ones measured in the foreground cleaned SMICA released by the Planck Collaboration. Our results show that Extended Theories of Gravity explain the dynamics of self-gravitating systems at cluster scales and represent an alternative to dark matter haloes.